IS Lab

IS/Lab/Lab7/Pallier.py

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+import random
+from math import gcd
+from sympy import isprime, lcm
+
+
+def generate_prime(bits=512):
+    while True:
+        num = random.getrandbits(bits)
+        if isprime(num):
+            return num
+
+
+def generate_keypair(bits=512):
+    p = generate_prime(bits)
+    q = generate_prime(bits)
+
+    n = p * q
+    n_squared = n * n
+    lambda_n = lcm(p - 1, q - 1)
+
+    g = n + 1
+
+    def L(x):
+        return (x - 1) // n
+
+    mu = pow(L(pow(g, lambda_n, n_squared)), -1, n)
+
+    public_key = (n, g)
+    private_key = (lambda_n, mu)
+
+    return public_key, private_key
+
+
+def encrypt(public_key, plaintext):
+    n, g = public_key
+    n_squared = n * n
+
+    while True:
+        r = random.randint(1, n - 1)
+        if gcd(r, n) == 1:
+            break
+
+    ciphertext = (pow(g, plaintext, n_squared) * pow(r, n, n_squared)) % n_squared
+
+    return ciphertext
+
+
+def decrypt(public_key, private_key, ciphertext):
+    n, g = public_key
+    lambda_n, mu = private_key
+    n_squared = n * n
+
+    def L(x):
+        return (x - 1) // n
+
+    plaintext = (L(pow(ciphertext, lambda_n, n_squared)) * mu) % n
+
+    return plaintext
+
+
+def homomorphic_add(public_key, ciphertext1, ciphertext2):
+    n, g = public_key
+    n_squared = n * n
+
+    result = (ciphertext1 * ciphertext2) % n_squared
+
+    return result
+
+
+def main():
+    print("Paillier Encryption Scheme Implementation\n")
+
+    print("Generating keypair...")
+    public_key, private_key = generate_keypair(bits=512)
+    print("Keys generated successfully.\n")
+
+    m1 = 15
+    m2 = 25
+    print(f"Original integers: {m1} and {m2}")
+    print(f"Expected sum: {m1 + m2}\n")
+
+    print("Encrypting integers...")
+    c1 = encrypt(public_key, m1)
+    c2 = encrypt(public_key, m2)
+    print(f"Ciphertext of {m1}: {c1}")
+    print(f"Ciphertext of {m2}: {c2}\n")
+
+    print("Performing homomorphic addition on encrypted values...")
+    c_sum = homomorphic_add(public_key, c1, c2)
+    print(f"Encrypted sum: {c_sum}\n")
+
+    print("Decrypting the result...")
+    decrypted_sum = decrypt(public_key, private_key, c_sum)
+    print(f"Decrypted sum: {decrypted_sum}\n")
+
+    if decrypted_sum == m1 + m2:
+        print("✓ Verification successful! The decrypted sum matches the original sum.")
+    else:
+        print("✗ Verification failed! The decrypted sum does not match.")
+
+
+if __name__ == "__main__":
+    main()